Applications of Fourier Analysis in Homogenization of the Dirichlet Problem: Lp Estimates

Abstract

Let uɛ be a solution to the system(Formula presented.), (Formula presented.), where (Formula presented.), is a smooth uniformly convex domain, and g is 1-periodic in its second variable, and both Aɛ and g are sufficiently smooth. Our results in this paper are twofold. First we prove Lp convergence results for solutions of the above system and for the non oscillating operator Aε(x)=A(x), with the following convergence rate for all 1 ≦ p